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%I #20 Sep 06 2017 20:13:17
%S 3,12,30,57,93,138,192,255,327,408,498,597,705,822,948,1083,1227,1380,
%T 1542,1713,1893,2082,2280,2487,2703,2928,3162,3405,3657,3918,4188,
%U 4467,4755,5052,5358,5673,5997,6330,6672,7023,7383,7752
%N 3 times centered triangular numbers: 9*n*(n+1)/2 + 3.
%H G. C. Greubel, <a href="/A164013/b164013.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = a(n-1) + 9*n (with a(0)=3). - _Vincenzo Librandi_, Nov 30 2010
%F a(0)=3, a(1)=12, a(2)=30, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - _Harvey P. Dale_, Mar 26 2015
%F From _G. C. Greubel_, Sep 06 2017: (Start)
%F G.f.: 3*(1 + x + x^2)/(1 - x)^3.
%F E.g.f.: (3/2)*(2 + 6*x + 3*x^2)*exp(x). (End)
%t LinearRecurrence[{3,-3,1},{3,12,30},50] (* _Harvey P. Dale_, Mar 26 2015 *)
%o (PARI) a(n)=9*binomial(n+1,2)+3 \\ _Charles R Greathouse IV_, Jul 17 2011
%Y Cf. A005448, A045943, A108099, A164015, A164016.
%K easy,nonn
%O 0,1
%A _Omar E. Pol_, Nov 07 2009
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